ceiling fan wiring

Hi, newbie to the forum, and very basic skill set for DIY projects, so please be kind, and keep it simple... I took down an old ceiling fan/light today, neglecting to note which wires were connected to which wires. The old fixture had pull chains, one for fan, one for light. There was a wall switch connected, however it only controlled power to the light.
WALL SWITCH
On the wall switch there were two black wires connected to the bottom terminal screw, one red wire connected to the top terminal screw. There are what appears to be three white wires behind the wall switch, in the wall switch box, in the back of the box, but I cannot determine what or how or if they are connected to anything by looking behind the switch.
CEILING BOX
On the ceiling box, there are three black wires twisted together, three white wires twisted together and one red wire.

NEW FAN/LIGHT FIXTURE
Hunter Stratford, one black wire, one black/white wire, one white wire. Green pigtail on fixture mounting plate (ground I assume). The old fan/light fixture had a blue wire just for the light, but the new fixture connects internally with its own plug to the fan. How do I connect the new fan/light and switch?

ceiling fan wiring

Thank you for the suggestions, I will try after today. However, can you tell me why there are three black wires coming down though the ceiling box, but only two black wires at the switch? Also, do I untwist the wires before adding the fixture wire to each bundle, or do I just add the fixture wire to the already twisted wires?